1) 3. Judicial, Executive, Legislative.
2) Trick question---Hamilton was never president. As RBG will tell, he was the first Secretary of the Treasury.
3) Article 4 section IV: "The United States shall guarantee to every state in this union a Republican form of government"
4) (The first 10 amendments are also known as "The Bill Of Rights", and was needed to get the Constitution ratified by the 13 states) Amendment 10---"The powers NOT delegated to the United States by the Constitution nor prohibited by it to the states, are reserved to the states respectively, or to the people"
6) None. Nowhere.
8) Executive, but don't feel bad if you said Legislative. The VP is President of the Senate, which is part of the Legislature, and has a vote in the event of a tie.